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//
// Copyright 2012 Hakan Kjellerstrand
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
using System;
using Google.OrTools.ConstraintSolver;
public class MagicSquare
{
/**
*
* Solves the Magic Square problem.
* See http://www.hakank.org/or-tools/magic_square.py
*
*/
private static void Solve(int n = 4, int num = 0, int print = 1)
{
Solver solver = new Solver("MagicSquare");
Console.WriteLine("n: {0}", n);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n * n, "x");
// for the branching
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
long s = (n * (n * n + 1)) / 2;
Console.WriteLine("s: " + s);
IntVar[] diag1 = new IntVar[n];
IntVar[] diag2 = new IntVar[n];
for (int i = 0; i < n; i++)
{
IntVar[] row = new IntVar[n];
for (int j = 0; j < n; j++)
{
row[j] = x[i, j];
}
// sum row to s
solver.Add(row.Sum() == s);
diag1[i] = x[i, i];
diag2[i] = x[i, n - i - 1];
}
// sum diagonals to s
solver.Add(diag1.Sum() == s);
solver.Add(diag2.Sum() == s);
// sum columns to s
for (int j = 0; j < n; j++)
{
IntVar[] col = new IntVar[n];
for (int i = 0; i < n; i++)
{
col[i] = x[i, j];
}
solver.Add(col.Sum() == s);
}
// all are different
solver.Add(x_flat.AllDifferent());
// symmetry breaking: upper left is 1
// solver.Add(x[0,0] == 1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_CENTER_VALUE);
solver.NewSearch(db);
int c = 0;
while (solver.NextSolution())
{
if (print != 0)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
Console.Write(x[i, j].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine();
}
c++;
if (num > 0 && c >= num)
{
break;
}
}
Console.WriteLine("\nSolutions: {0}", solver.Solutions());
Console.WriteLine("WallTime: {0}ms", solver.WallTime());
Console.WriteLine("Failures: {0}", solver.Failures());
Console.WriteLine("Branches: {0} ", solver.Branches());
solver.EndSearch();
}
public static void Main(String[] args)
{
int n = 4;
int num = 0;
int print = 1;
if (args.Length > 1)
{
n = Convert.ToInt32(args[1]);
}
if (args.Length > 2)
{
num = Convert.ToInt32(args[2]);
}
if (args.Length > 3)
{
print = Convert.ToInt32(args[3]);
}
Solve(n, num, print);
}
}